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Creators/Authors contains: "Bresch, Didier"

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  1. ; ; (, Analysis & PDE)
    Free, publicly-accessible full text available January 1, 2026
  2. ; ; (, Communications in Applied and Industrial Mathematics)
    Abstract This paper concerns the existence of global weak solutionsá la Lerayfor compressible Navier–Stokes–Fourier systems with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically unstable. More precisely, the main novelty is that the pressure law is not assumed to be monotone with respect to the density. This provides the first global weak solutions result for the compressible Navier-Stokes-Fourier system with such kind of pressure law which is strongly used as a generalization of the perfect gas law. The paper is based on a new construction of approximate solutions through an iterative scheme and fixed point procedure which could be very helpful to design efficient numerical schemes. Note that our method involves the recent paper by the authors published in Nonlinearity (2021) for the compactness of the density when the temperature is given. 
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  3. ; ; (, Journal of the European Mathematical Society)
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  4. ; ; (, Nonlinearity)
    Abstract This paper concerns the existence of global weak solutions à la Leray for compressible Navier–Stokes equations with a pressure law which depends on the density and on time and space variables t and x . The assumptions on the pressure contain only locally Lipschitz assumption with respect to the density variable and some hypothesis with respect to the extra time and space variables. It may be seen as a first step to consider heat-conducting Navier–Stokes equations with physical laws such as the truncated virial assumption. The paper focuses on the construction of approximate solutions through a new regularized and fixed point procedure and on the weak stability process taking advantage of the new method introduced by the two first authors with a careful study of an appropriate regularized quantity linked to the pressure. 
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  5. ; ; (, Comptes Rendus Mathematique)
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  6. ; (, Annals of Mathematics)
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